Archimedean spiral

From https://en.wikipedia.org/wiki/Archimedean_spiral

using GMT
# Play arround with these parameters
T = 1;
omega = omega = 2pi / T;
v = 0.2;
t = 0:0.01:5pi;
x = v.*t .* cos.(omega .* t);
y = v.*t .* sin.(omega .* t);
plot(x, y, aspect=:equal, show=true)

Fermati spiral

Draw a Polar scatter plot with variable symbol size, color and transparency. We will use the default color scale (turbo) and fig size (12 cm).

using GMT
teta = 0:0.01:5pi;
xf = sqrt.(teta) .* cos.(teta);
yf = sqrt.(teta) .* sin.(teta);
plot(xf,yf, aspect=:equal, show=true)


From This FEX contribution. The author here wanted to reflect the fact that on a sunflower the seeds close to the center are smaller and have a higher density.

using GMT
phi = (sqrt(5)-1)/2;
n = 2618;
rho = (2:n-1) .^ phi;
theta = (2:n-1)*2pi*phi;
scatter(rho .* cos.(theta), rho .* sin.(theta), marker=:point, aspect=:equal, show=true)

Another Sunflower

This one was reversed from the javascript in this page, which follows the original work of Helmut Vogel inA better Way to Construct the Sunflower Head, where he proposed that spiral branches of seeds in a sunflower head are added from the center at an angle of 137.5∘ from the preceding one.

This time we will also color the seed points in function of r, the distance to the center and pain with a dark background.

using GMT
angle = 137.5;	# Play with this angle between [137.0 138.0]. Amazing the effect, no?
alfa = 2pi * angle / 360;
n_seeds = 1500;
seeds = 0:n_seeds;
r = sqrt.(seeds);
ϕ = alfa * seeds;
C = makecpt(range=(1,sqrt(n_seeds),1), cmap=:buda);	# Color map to paint the seeds
scatter(r .* cos.(ϕ), r .* sin.(ϕ), marker=:point, cmap=C, zcolor=r,
        frame=(fill=20,), aspect=:equal, show=true)